Prestack Seismic Inversion for VTI Media Using Weak-Contrast PP-Reflectivity Derived From Elastic Impedance Matrices

The transversely isotropic media with a vertical symmetry (VTI) has been widely used in shale reservoirs, and the reflection response and prestack seismic inversion have been of interest to geophysicists. Petrophysical experiments have shown that shale reservoirs may exhibit moderate or even stronger anisotropy, causing limitations in the weak anisotropy-based reflectivity approximation. Existing weak-contrast approximations are usually highly nonlinear equations characterized by the stiffness parameters and slowness, which is not conducive to AVO analysis and prestack seismic inversion of anisotropic parameters. We proposed a novel approach for weak-contrast PP-reflectivity based on the P- and S-elastic impedance matrices and applied it to prestack seismic inversion. First, by simplifying the phase velocities and polarization vectors, the elastic impedance matrices are linearly characterized in the weak-contrast half-spaces. Then, the perturbation theory is used to derive the weak-contrast PP-reflectivity, which consists of two terms, one directly resulting from the difference between the parameters of upper and lower media, and the other resulting from the first-order perturbation of the phase velocity and polarization. It has a clear physical meaning and can degenerate to the Aki-approximation in isotropic media. In particular, the isotropic second-order terms are introduced to significantly improve its accuracy at the interfaces with high-speed contrast. Furthermore, we designed a coefficient matrix to linearize the high-order reflectivity terms and developed an improved algorithm based on the alternating direction method of multipliers (ADMMs). Finally, the applications on logging curves and field seismic data for the shale prove the feasibility and effectiveness of the proposed method.